What to Expect on the Math Portion of the ACT
Test Format:
There are 60 questions and you have 60 minutes to complete this portion.
The questions are broken down as follows:
Pre- algebra – 14 questions
Elementary Algebra – 10 questions
Intermediate Algebra – 9 questions
Coordinate Geometry – 9 questions
Plane Geometry – 14 questions
Trigonometry – 4 Questions
NOTES/ TIPS:
o All questions are of equal weight
o You are NOT penalized for guessing
o Pace Yourself
o Don’t leave questions blank at the end
o Mark up your exam
 Circle if don’t finish
 Cross of problems you can rule out
o Check your answers if you do have time left
o Can use a calculator
 Check that yours is working with batteries
 Can not share
 Make sure you know how to use it
ALGEBRA – Pre-Algebra
(14 Questions)
1) Properties of Numbers
EXAMPLE:
Which one of the following expressions has an even integer value for all integers a and c ?
A. 8a + 2ac
B. 3a + 3c
C. 2a + c
D. a + 2c
E. ac + a2
2) Arithmetic Operations (using fractions, whole numbers, and decimals)
EXAMPLE:
43 + (5 × 3) - 2 = ?
A. 42
B. 56
C. 289
D. 337
E. 481
3) Factors
EXAMPLE:
What is the greatest common factor of 42, 126, and 210 ?
A. 2
B. 6
C. 14
D. 21
E. 42
4) Ratios, Proportions and Percents
EXAMPLE:
A typical high school student consumes 67.5 pounds of sugar per year. As part of a new nutrition plan, each
member of a track team plans to lower the sugar he or she consumes by at least 20% for the coming year.
Assuming each track member had consumed sugar at the level of a typical high school student and will adhere
to this plan for the coming year, what is the maximum number of pounds of sugar to be consumed by each track
team member in the coming year?
A. 14
B. 44
C. 48
D. 54
E. 66
5) Exponents
EXAMPLE:
Which of the following is equivalent to (x)(x)(x)(x3), for all x?
A. 4x
B. 6x
C. x6
D. 4x6
E. 4x4
6) Scientific Notation
EXAMPLE:
A particle travels 1 x 106 meters per second in a straight line for 5 x 10-6 seconds. How many meters has it
traveled?
A. 2 x 1011
B. 5 x 1012
C. 5 x 10-12
D. 5
E. 5 x 10-36
7) Square Roots
EXAMPLE:
Which of the following is equal to √45 ?
A) 15
B) 5√3
C) 9√5
D) 3√5
E) 3
8) Absolute Value
EXAMPLE:
|5 - 2| - |6 - 9| = ?
A. 6
B. 0
C. -8
D. 22
E. -6
9) Linear Equations in 1 Variable
EXAMPLE:
What is the value of x when 2x + 3 = 3x – 4 ?
A. –7
B.
C. 1
D.
E. 7
10) Simple Probability and Counting Techniques
EXAMPLE:
What is the probability that a number selected at random from the set {2, 3, 7, 12, 15, 22, 72, 108} will be
divisible by both 2 and 3 ?
A.
B.
C.
D.
E.
11) Simple Descriptive Statistics
EXAMPLE:
The distribution of Jamal’s high school grades by percentage of course credits is given in the circle graph
below. What is Jamal’s grade point average if each A is worth 4 points; each B, 3 points; and each C, 2 points?
A. 3.0
B. 3.4
C. 3.6
D. 3.7
E. Cannot be determined from the given information
ALGEBRA – Elementary Algebra
(10 Questions)
1) Evaluate Algebraic Expressions with Substitution
EXAMPLE:
If a = 3, then 2 / (1/7 + 1/a) = ?
A) 5
B) 21/10
C) 20
D) 10
E) 21/5
2) Use Variables to Express Functional Relationships
EXAMPLE:
Which of the following equations represents the linear relationship between time, t, and velocity, v,
shown in the table below?
A.
B.
C.
D.
E.
T
0
1
2
V
120
152
184
v = 32t
v = 32t + 120
v = 120t
v = 120t + 32
v = 120t + 120
3) FOIL and Factor
EXAMPLE:
Which of the following is a factor of the polynomial 2x2 – 3x – 5 ?
A. x – 1
B. 2x – 3
C. 2x – 5
D. 2x + 5
E. 3x + 5
4) Exponents and Square Roots
5) Understanding Algebraic Expressions
EXAMPLE:
For all nonzero real numbers p, t, x, and y such that
, which of the following expressions is
equivalent to t ?
A.
B.
C.
D.
E.
ALGEBRA – Intermediate Algebra
(9 Questions)
1) Quadratic Formula
2) Rational and Radical Expressions
EXAMPLE:
Which of the following is equivalent to
?
A.
B.
C.
D.
E.
3) Absolute Value and Inequalities
EXAMPLE:
What are the values of a and b, if any, where - a|b + 4| > 0?
A) a > 0 and b ≠ -4
B) a > 0 and b ≠ 4
C) a < 0 and b ≥ -4
D) a < 0 and b ≠ -4
E) a < 0 and b ≤ -4
4) Basic Sequences and Patterns
EXAMPLE:
What is x, the second term in the geometric series
+x+
+
+…?
A.
B.
C.
D.
E.
5) Systems of Equations
EXAMPLE:
When graphed in the (x,y) coordinate plane, at what point do the lines 2x + 3y = 5 and x = -2 intersect?
A) (-2,0)
B) (-2,5)
C) (0,5/3)
D) (0,5)
E) (-2,3)
6) Quadratic Inequalities
7) Functions and Modeling
EXAMPLE:
Each side of the smaller square in the figure below is x inches long, and each side of the larger square is
c inches longer than a side of the smaller square. The area of the larger square is how many square
inches greater than the area of the smaller square?
A. c2
B. Xc
C. 4c
D. (x + c)2
E. 2xc + c2
8) Matrices
9) Complex Numbers
EXAMPLE:
=?
A. 9i
B. 9 + i
C. 9 – i
D. 9
E. –9
10) Roots
EXAMPLE:
What is the x-intercept of the graph of y = x2 – 4x + 4 ?
A. –2
B. –1
C. 0
D. 1
E. 2
GEOMETRY – Coordinate Geometry
(9 Questions)
1) Equations and Graphs (points, lines and planes)
EXAMPLE:
In the standard (x, y) coordinate plane below, 3 of the vertices of a rectangle are shown. Which of the
following is the 4th vertex of the rectangle?
A. (3,–7)
B. (4,–8)
C. (5,–1)
D. (8,–3)
E. (9,–3)
2) Slope
EXAMPLE:
What is the slope of any line parallel to the line 9x + 4y = 7 ?
A. –9
B.
C.
D. 7
E. 9
3) Parallel and Perpendicular Lines
EXAMPLE:
Which of the lines below is not parallel to the line 6x - 2y = 10?
A) 3x - y = 7
B) -6x + 2y = 20
C) 3x + y = 7
D) 6x - 2y = 5
E) x - y/3 = 9
4) Distance and Midpoint
EXAMPLE:
A boat departs Port Isabelle, Texas, traveling to an oil rig. The oil rig is located 9 miles east and
12 miles north of the boat’s departure point. About how many miles is the oil rig from the departure
point?
A. 3
B.
C. 15
D. 21
E. 225
5) Properties of a Circle
EXAMPLE:
Which of the following is an equation of the circle with its center at (0,0) that passes through (3,4) in the
standard (x,y) coordinate plane?
A. x – y = 1
B. x + y = 25
C. x2 + y = 25
D. x2 + y2 = 5
E. x2 + y2 = 25
6) Pythagorean Theorem
EXAMPLE:
If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the
other leg?
A) 5
B) 5√3
C) 5√5
D) 75
E) 10 - √5
7) Graphing Inequalities
8) Conics
GEOMETRY – Plane Geometry
(14 Questions)
1) Angles and Lines:
2) Properties of :
a. Circles
EXAMPLE:
A circle has a circumference of 16 feet. What is the radius of the circle, in feet?
A.
B. 4
C. 8
D. 16
E. 32
b. Triangles
c. Rectangles
EXAMPLE:
A rectangle with a perimeter of 30 centimeters is twice as long as it is wide. What is the area of
the rectangle in square centimeters?
A. 15
B. 50
C. 200
D. 3
E. 6
d. Parallelograms
EXAMPLE:
In quadrilateral PQRS below, sides PS and QR are parallel for what value of x ?
A. 158
B. 132
C. 120
D. 110
E. 70
e. Trapeziods
EXAMPLE:
The area of a trapezoid is 0.5 h (b1 + b2), where h is the altitude, and b1 and b2 are the lengths of
the parallel bases. If a trapezoid has an alitude of 15 inches, an area of 105 square inches, and
one of the bases 22 inches, what is the perimeter, in inches, of the trapezoid?
A) 8
B) 45
C) 60
D) 30
E) This trapezoid does not exist.
3) Transformations
4) Proof and Proof Techniques
5) Volume and 3D Applications
EXAMPLE:
The volume, V, of the right circular cone with radius r and height h, shown below, can be found using
the formula V =
r2h. A cone-shaped paper cup has a volume of 142 cubic centimeters and a height
of 8.5 centimeters. What is the radius, to the nearest centimeter, of the paper cup?
A. 2
B. 4
C. 8
D. 12
E. 16
TRIGONOMETRY
(4 Questions)
1) SOH CAH TOA
EXAMPLE: Which of the following is the sine of A in the right triangle below?
A.
B.
C.
D.
E.
2) Solving Triangles
EXAMPLE:
Which of the following expressions is the closest approximation to the height h, in feet, of the roof truss shown
below?
A. 15 tan 20°
B. 15 sin 20°
C. 30 tan 20°
D. 30 sin 20°
E.
3) Trigonometric Identities
EXAMPLE:
Which of the following is equivalent to sin csc(– ) wherever sin csc(– ) is defined?
A. –1
B. 1
C. –tan
D. tan
E. –sin2
4) Solving Trig Equations
EXAMPLE:
If sin,2x = sin,x, then which of the following could NOT be true?
A. x = 0
B. x =
C. cos,x =
D. sin, x = 0
E. cos,x = 0
5) Graphing Trig Equations
What if I don’t have a Clue?
******NOTE******
THESE HINTS DO NOT ALWAYS WORK. They may help if you really have no idea how to solve
the problem. If you have solved the problem and it does not seem to go along with these, GO
WITH YOUR ANSWER!!
1) Rule out options – remember they try to trick you!!
2) Pictures are often drawn to scale (even if they say they are not)
3) Lists of Numbers – select a middle number
4) Solving, simplifying, reduce, – plug in a number
EXAMPLES:
1. 2x2 -10x + 12 =
a) (2x -3) (x – 4)
b) [2 (x – 3)2]
c) 2(x - 2)(x - 3)
d) 2(x + 6)(x-1)
e) 2x(x - 5)(x – 1)
2. Where defined
a) -3xy4
b) -3xy2
c) xy 4
18𝑥 3 𝑦 8 𝑧
−6𝑥 2 𝑦 4 𝑧
=
3
d)
1
3 xy 2
e) y 4
3x
3. Reduce to lowest terms, 2 x 2  3x  2
a) 2 x  1
10  x  3x 2
5  3x
b) 1  2 x
3x  5
c) 2 x  1
3x  5
d) 2 x  1
3x  5
e)  2 x  1
3x  5
5) Convert square roots or pi’s to decimals.